The current abundance of sequenced and annotated genomes shows that their partitioning in different functional classes often yields astonishing common properties. For example, genomes of the same size tend to produce the same number of protein families regardless of their evolutionary distance. Clearly, the trends bringing to this collective behavior must transcend at least some of the specificity of the evolutionary adaptation of a genome (which depend on lifestyle, niche, environment of the organism). Rather, they must be the product of some more "universal" aspects of evolution. This seminar will address some examples of scaling laws for different genomic observables, related to protein domain topologies and their functional annotations, and explore minimal models that can provide "thermodynamic" explanations of the scaling laws, using the ingredients of statistical mechanics.